In this paper, we discuss a stochastic approach to wavefield reconstruction inversion [1]}, referred to as WaRIance in the remainder of this paper. WRI was originally conceived an an alternative to full-waveform inversion [2]} that relaxes the convergence requirements on the initial model. The adoption of WRI at large has been curbed by the computational demands required to solve the so-called “augmented” wave equation, for which direct or iterative solution methods are quite challenging in 3D. The literature around WRI is now extensive, the references most relevant for our work being [3]}, [4]}, [5]}, [6]}. Only few works had attempted to overcome the computational issues of conventional WRI, for example [3]} and [8]}. Recently, the authors presented a version of WRI where the augmented wavefield is approximated in a sensible manner [9]}, albeit with some drawbacks in terms of reconstruction quality and computational overhead. This project can be seen as a way to improve on [9]}. The WaRIance technique here proposed retains the classical well-conditioning properties of WRI in terms of local minimum stagnation, but also can reasonably scale to large 3D problems.
